Testing for departures from nominal dispersion in generalized nonlinear models with varying dispersion and/or additive random effects

Abstract

This paper discusses the tests for departures from nominal dispersion in the framework of generalized nonlinear models with varying dispersion and/or additive random effects. We consider two classes of exponential family distributions. The first is discrete exponential family distributions, such as Poisson, binomial, and negative binomial distributions. The second is continuous exponential family distributions, such as normal, gamma, and inverse Gaussian distributions. Correspondingly, we develop a unifying approach and propose several tests for testing for departures from nominal dispersion in two classes of generalized nonlinear models. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas, so that the tests can easily be implemented using existing statistical software. The properties of test statistics are investigated through Monte Carlo simulations.

Keywords:

• Departures from nominal dispersion
• Exponential family nonlinear models
• Generalized nonlinear models
• Random effects
• Score test
• Varying dispersion

Acknowledgements

The project supported by NSFC(10671032). The authors gratefully acknowledge the editor, associate editor, and referee for their valuable comments and suggestions that substantially improved the representation.